A class of interconnected neural networks composed of generalized Brain-State-in-a-Box (gBSB) neural subnetworks is considered. Interconnected gBSB neural network architectures are proposed along with their stability conditions. The design of the interconnected neural networks is reduced to the problem of solving linear matrix inequalities (LMIs) to determine the interconnection parameters. A method for solving LMIs is devised generating the solutions that, in general, are further away from zero than the corresponding solutions obtained using MATLAB's LMI toolbox, thus resulting in stronger interconnections between the subnetworks. The proposed architectures are then used to construct neural associative memories. Simulations are performed to illustrate the results obtained.